Question

Write the expression as the sine, cosine, or tangent of an angle. sin 5x cos x - cos 5x sin x

Answer 1

sin 5x cos x - cos 5x sin x = sin(4x)

Explanation:

Given that the trigonometric expression,

sin 5x cos x - cos 5x sin x

Here we use the "sum and difference formulas"

Sum and Difference Formulas

sin(A+B)=sin A cos B + cos A sin B

sin(A-B)=sin A cos B - cos A sin B

cos(A+B)=cos A cos B - sin A sin B

cos(A-B)=cos A cos B + sin A sin B

So,

sin 5x cos x - cos 5x sin x = sin (5x - x)

sin 5x cos x - cos 5x sin x = sin(4x)

That's the final answer.